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State-space Construction of Hybrid Petri Nets with Multiple Stochastic Firings

Authors:

Patricia Schinke,

Henner Niehaus,

Joanna Delicaris,

Anne RemkeAuthors Info & Claims

ACM Transactions on Modeling and Computer Simulation (TOMACS), Volume 31, Issue 3

Article No.: 13, Pages 1 - 37

https://doi.org/10.1145/3449353

Published: 24 August 2021 Publication History

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Abstract

Hybrid Petri nets have been extended to include general transitions that fire after a randomly distributed amount of time. With a single general one-shot transition the state space and evolution over time can be represented either as a Parametric Location Tree or as a Stochastic Time Diagram. Recent work has shown that both representations can be combined and then allow multiple stochastic firings. This work presents an algorithm for building the Parametric Location Tree with multiple general transition firings and shows how its transient probability distribution can be computed using multi-dimensional integration. We discuss the (dis-)advantages of an interval arithmetic and a geometric approach to compute the areas of integration. Furthermore, we provide details on how to perform a Monte Carlo integration either directly on these intervals or convex polytopes, or after transformation to standard simplices. A case study on a battery-backup system shows the feasibility of the approach and discusses the performance of the different integration approaches.

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Cited By

Niehage MRemke A(2024)The Best of Both Worlds: Analytically-Guided Simulation of HPnGs for Optimal ReachabilityPerformance Evaluation Methodologies and Tools10.1007/978-3-031-48885-6_5(61-81)Online publication date: 3-Jan-2024
https://doi.org/10.1007/978-3-031-48885-6_5
Stübbe JRemke A(2024)Monte-Carlo Integration on a Union of PolytopesGraphs and Combinatorial Optimization: from Theory to Applications10.1007/978-3-031-46826-1_12(147-160)Online publication date: 23-Feb-2024
https://doi.org/10.1007/978-3-031-46826-1_12
Da Silva CSchupp SRemke A(2023)Optimizing Reachability Probabilities for a Restricted Class of Stochastic Hybrid Automata via Flowpipe ConstructionACM Transactions on Modeling and Computer Simulation10.1145/360719733:4(1-27)Online publication date: 26-Oct-2023
https://dl.acm.org/doi/10.1145/3607197

Index Terms

State-space Construction of Hybrid Petri Nets with Multiple Stochastic Firings
1. Theory of computation
  1. Logic
    1. Verification by model checking

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cover image ACM Transactions on Modeling and Computer Simulation

ACM Transactions on Modeling and Computer Simulation Volume 31, Issue 3

Special Issue on Qest 2019

July 2021

149 pages

ISSN:1049-3301

EISSN:1558-1195

DOI:10.1145/3476822

Editor:
Francesco Quaglia
University of Rome Tor Vergata, Italy

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Copyright © 2021 ACM.

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Publication History

Published: 24 August 2021

Accepted: 01 February 2021

Revised: 01 September 2020

Received: 01 March 2020

Published in TOMACS Volume 31, Issue 3

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Cited By

Niehage MRemke A(2024)The Best of Both Worlds: Analytically-Guided Simulation of HPnGs for Optimal ReachabilityPerformance Evaluation Methodologies and Tools10.1007/978-3-031-48885-6_5(61-81)Online publication date: 3-Jan-2024
https://doi.org/10.1007/978-3-031-48885-6_5
Stübbe JRemke A(2024)Monte-Carlo Integration on a Union of PolytopesGraphs and Combinatorial Optimization: from Theory to Applications10.1007/978-3-031-46826-1_12(147-160)Online publication date: 23-Feb-2024
https://doi.org/10.1007/978-3-031-46826-1_12
Da Silva CSchupp SRemke A(2023)Optimizing Reachability Probabilities for a Restricted Class of Stochastic Hybrid Automata via Flowpipe ConstructionACM Transactions on Modeling and Computer Simulation10.1145/360719733:4(1-27)Online publication date: 26-Oct-2023
https://dl.acm.org/doi/10.1145/3607197

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